Webcourse (1999) - Quantum Approaches to Understanding the Mind

8/16/2019 Webcourse (1999) - Quantum Approaches to Understanding the Mind

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Lecture, Week 1: September 27th - October 3rd, 1999

Outline

1. What is consciousness? An ancient debate2. The study of consciousness in the 20th century

3. The prevalent view: computational emergence

4. The quantum approach to consciousness

5. Conclusion: Is consciousness due to computational emergence or fundamental

quantum process?

1. What is consciousness? An ancient debate

How does brain activity produce conscious experience? Why do we feel love, hear a

flute, see a purple sunset? Philosophers call the raw components which comprise

conscious experience qualia (e.g. Chalmers,1996).

It is not at all obvious why we need qualia from an evolutionary standpoint---complex,

adaptive behavior of unfeeling zombie-like creatures might well have enabled them toflourish. However it seems unlikely that, for example, a zombie could have painted the

Mona Lisa. So what are these raw feelings? What is consciousness?

Since ancient Greece there have been two types of explanations. On the one hand

Socrates said that conscious mental phenomena were "products of the cerebrum"---

produced by activities in the brain. On the other hand Democritus believed mental

phenomena were fundamental "features of reality", merely accessed by the brain.

Figure 1. Are mental 'qualia' like the redness of a rose, patterns of activitywithin the brain, or a fundamental feature of nature?

2. The study of consciousness in the 20th century

In the past hundred years scientific pursuit of consciousness has had its ups and downs.

William James's 1903 "Principles of Psychology" had placed the topic at center stage, but

then for most of the century behaviorist psychology relegated consciousness to a role as

irrelevant epiphenomenon. Neurophysiologists kept the term consciousness alive during

these "Dark Ages", and in the 1960's and 1970's cognitive functions became correlated

with the brain's inner states. Nevertheless the "C-word" remained slightly off-color:

"Why discuss something that can't be measured?" In the 1990's much of this changed and

the problem of consciousness became a hot topic spanning many fields. As the milleniumnears, consciousness is coming to the forefront of scientific frontiers.

There are numerous reasons for the late 20th century consciousness boom, but credit

justifiably goes to scholarly and passionate books written by luminaries such as Roger

Penrose (198 9; 1994), Francis Crick (1994), John Eccles (1989) and Gerald Edelman

(1989) who each digressed from primary fields to address their intimate mystery. These

noble efforts were preceded by Marcel and Bisiach's anthology Consciousness in


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Contemporary Science (1988) and Bernard Baar's A Cognitive Theory of Consciousness

(1988).

Within philosophy a focus of disagreement regarding the nature of conscious experience

developed in the 1970's and 1980's. "Anti-physicalists" questioned how conscious

experience could be derived from ordinary matter (a view derived from Socrates and

espoused in slightly varying forms by"reductionists/functionalists/materialists/physicalists"). The key figures producing this

anti-physicalist pressure were Saul Kripke (1972), Thomas Nagel (1974) and Frank

Jackson (1982). On the other side Patricia Churchland (1986), Paul Churchland (1989)

and others steadied the flag of physicalism, and Daniel Dennett's flamboyantly titled

Consciousness Explained (1991) pushed it overboard by arguing conscious experience

out of existence. However David Chalmers' The Conscious Mind (1996) illuminated the

chasm between physicalist explanations and the facts about consciousness (the "hard

problem"), and suggested conscious experience may be an irreducible, fundamental

property of reality (Rosenberg, 1997).

3. The prevalent view: computational emergence

Despite some anti-physicalist pressure, the modern version of Socrates' view is thecurrently dominant scientific position. Conventional explanations portray consciousness

as an emergent property of computer-like activities in the brain's neural networks. The

brain is essentially a computer, and neuronal excitations (axonal firings/synaptic

signaling) are fundamental information states, or "bits" equivalent to either 1 or 0. The

prevailing views among scientists in this camp are that 1) patterns of neural network

activities correlate with mental states, 2) synchronous network oscillations in thalamus

and cerebral cortex temporally bind information, and 3) consciousness emerges as a

novel property of computational complexity among neurons.

Figure 2. PET scan image of brain showing visual and audit ory recognition (from S Petersen,

Neuroimaging Laboratory, Washington University, St. Louis. Also see J.A. Hobson

"Consciousness," Scientific American Library, 1999, p. 65).

Yet computers aren't conscious, at least as far as we can tell. To explain how qualia and

consciousness may be produced by complex interactions among simple neurons,

proponents of emergence theory point out that it is quite common in nature for complex

interactions among many simple states to lead to higher order emergence of phases with

novel properties. Examples include a candle flame, whirlpool, or the Great Red Spot on

Jupiter. Could conscious experience be such an emergent, novel property? (See AlwynScott's "Stairway to the Mind" for an elegant exposition of the emergence argument).

Figure 3. Electrophysiological correlates of consciousness.


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But weather patterns and other known emergent phenomena aren' t conscious either.

Complex neuronal interactions are indeed essential to our form of consciousness, and do

appear to correlate with conscious experience. But at what critical level of computational

complexity does consciousness emerge? Why do the emergent properties have qualia? Is

some purely biological factor necessary for the emergence of conscious experience? Or

are deeper level factors in play?For a debate between Alwyn Scott and Stuart Hameroff on the merits of emergence

theory vs quantum a pproaches to explain consciousness, see the article "Sonoran

afternoon" in the Tucson II book, and at

~http://www.u.arizona.edu/~hameroff/sonoran.html

In addition to 'qualia' computational emergence approaches appear to fall short in fully

explaining other enigmatic features of consciousness:

• The nature of subjective experience, or 'qualia'- our 'inner life' (Chalmers' "hard

problem");

• Subjective binding of spatially distributed brain activities into unitary objects in

vision, and a coherent sense of self, or 'oneness';• Transition from pre-conscious processes to consciousness itself;

• Non-computability, or the notion that consciousness involves a factor which is

neither random, nor algorithmic, and that consciousness cannot be simulated

(Penrose, 1989, 1994, 1997);

• Free will;

• Subjective time flow.

• Apparent reverse time anomalies (e.g. Libet, Radin/Bierman)

As we shall see, these enigmatic features may be amenable to quantum approaches.

Another problem with computational emergence theory is that in fitting the brain to a

computational view, such explanations omit incompatible neurophysiological details:

•

Widespread apparent randomness at all levels of neural processes (is it really

noise, or underlying levels of complexity?);

• Glial cells (which account for some 80% of brain);

• Dendritic-dendritic processing;

• Electrotonic gap junctions;

• Cytoplasmic/cytoskeletal activities; and,

• Living state (the brain is alive!).

A further difficulty is the absence of testable hypotheses in emergence theory. No

threshold or rationale is specified; rather, consciousness "just happens".

Finally, the complexity of individual neurons and synapses is not accounted for in such

arguments. Since many forms of motile single-celled organisms lacking neurons orsynapses are able to swim, find food, learn, and multiply through the use of their internal

cytoskeleton, can they be considered more advanced than neurons?


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Figure 4. Single cell paramecium can swim and avoid obstacles using its cytoskeleton.

It has no synapses. Are neurons merely simple switches?

4. The quantum approach to consciousness

An alternative to Socrates' view and that of current emergence theory stems from

Democritus who believed qualia to be primitive, fundamental aspects of reality,

irreducible to anything else. Philosophical renditions along these lines have included

panpsychism (e.g. Spinoza, 1677), panexperientialism (e.g. Whitehead, 1920) and most

recently pan-protopsychism (Chalmers, 19 95). Perhaps most compatible with modern

physics is Whitehead who believed consciousness to be a sequence of discrete events

("occasions of experience") occurring in a wider, proto-conscious field.(Abner Shimony

in 1993 pointed out that Whitehead's discrete events were consistent with quantum state

reductions.) (Lecture week 3)

Could Whitehead's "philosophical" proto-conscious field be the basic level of physical

reality? Do qualia exist as fundamental features of the universe (e.g. like spin or charge),

somehow accessed by brain processes to adorn neuronal activities with conscious

experience?

What physical features of the universe could relate to qualia? Can qualia be given a

physical correlate, say in modern descriptions of the fundamental nature of the universe?

Whether or not the fundamental nature of reality---empty space---is a true void or has

some underlying structure is a question which also dates to the Greeks. Democritus saw a

true void, while Aristotle saw a background pattern or "plenum" with 3 dimensions. In

the 17th century Galileo described the motion of free-falling objects, and Newton

discovered that the force of gravity between two objects depends on the mass of the

objects and the distance between them. But Newton couldn't understand how such a

mysterious force could operate in the absolute void he assumed empty space to be. In the

19th century Maxwell postulated a "luminiferous ether" as a background pattern to

explain the propagation of electromagnetic waves in a vacuum, but the Michelson-

Morley experiment seemed to rule out a background medium. Einstein's special relativityseemed to confirm the view of a true void with its lack of preferred reference frames,

although it did introduce the concept of a four dimensional universe in which the 3

dimensions of space are unified with the dimension of time.

Einstein's general relativity stated that a massive object such as the sun curves spacetime

around itself, much as a bowlingball would form a depression in a rubber sheet. Smaller

objects such as the earth and other planets move around the object like marbles would

roll down the depression in the rubber sheet. Therefore gravity was not a mysterious

force but curvatures in reality itself, what Einstein called the spacetime metric.

Figure 5. Einstein's spacetime metric describes the curvature of spacetime at large scales (Science

Year 2000).

Einstein's general relativity with its curvatures and spacetime metric swung the prevalent

scientific view back to an underlying pattern. But what exactly is the spacetime metric?

And what is happening at the smallest scales? We do know that at the level of the Planck


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scale (10 -33 cm, 10 -43 sec) spacetime is no longer smooth, but quantized. The nature of

reality at the level of atoms, sub-atomic particles and below remained mysterious. These

effects are approached through quantum mechanics, a branch of physics developed in the

early 1900's by Niels Bohr of Denmark, Erwin Schrodinger of Austria, and Werner

Heisenberg of Germany.Quantum mechanics explains how atoms absorb and give off

units of energy called quanta. Surprisingly, quanta act as both particles and waves, andcan exist in quantum superposition of two or more states or locations simultaneously!

While quantum mechanics cannot explain how this is possible, it can explain the

behavior of the various particles that make up atoms.

Physicists have developed a quantum theory known as the Standard Model of Particle

Physics to describe all of the fundamental particles that make up atoms.Protons and

neutrons which make up the atom's nucleus are themselves made up of tiny particles

called quarks. There are 6 kinds of quarks, and atoms also contain electrons that orbit the

nucelus. The Standard Model also describes the forces at work at the sub-atomic realm,

including the electromagnetic force (which holds atoms and molecules together), the

strong force (which holds protons and neutrons together), and the weak force (which

causes certain types of radioactive decay). The forces are carried by particle/waves called bosons, which include photons which carry the electromagnetic force. The Standard

Model predicts another as-yet-unobserved particle/wave, the Higgs boson which particle

physicists believe may give mass to particles. The Standard Model does not include a

description of gravity, which in the atomic realm is much weaker than the other forces.

Another odd feature of quantum particle/waves is quantum entanglement. If two quantum

partices are coupled but then go their separate ways, they remain somehow connected

over space and time. Measurement of one will affect the state of the other (Lecture Week

2). Also, quantum particles can condense into one collective quantum object in which all

components are governed by the same wave function (e.g. Bose-Einstein condensate).

But we don't see this quantum weirdness in our seemingly clasiscal world. Science has

one theory (general relativity) to describe the behavior of large masses such as planetsand pencils, and another theory (quantum mechanics) to explain the behavior of atoms

and sub-atomic particles. What is the cut-off between the quantum and classical worlds?

What is needed is a "unified theory" combining the large scale and the small scale. One

approach to a unified theory is found in Roger Penrose's view of the meaning of quantum

superposition. Quantum theory tells us that at small scales particles may have no definite

location or state, and exist in "superposition" of many possible states ("wave-particle

duality"). What does it mean to be in two or more states or locations simultaneously?

Could this property be relevant, or useful in understanding consciousness?

It turns out quantum superposition is indeed relevant to a new form of technological

computing - quantum computing. Could this property be relevant, or useful in

understanding consciousness? It turns out quantum superposition is indeed relevant to anew form of technological computing - quantum computing.


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Figure 6. Wave-particle duality of quantum objects is essential to quantum computing. A particle

has wave-like quantum behavior, and may also localize to a definite state/location. From "Explorati

ons in Quantum Computing", by Colin P. Williams and Scott H. Clearwater, Springer-Verlag, New

York, 1998

Quantum computing is a proposed technology which aims to take significant advantage

of features of quantum theory, and may connect brain activity to fundamental spacetime

geometry.Described theoretically in the 1980's (e.g. by Benioff, Feynman, Deutsch), "quantum

computing" is suggested to utilize quantum superposition, in which a particle can exist in

two or more states, or locations simultaneously. Whereas current computers represent

information as "bits" of either 1 or 0, quantum computers are proposed to utilize quantum

bits---"qubits"---of both 1 AND 0.

Potential advantages in quantum computing stem from qubits in superposition interacting

nonlocally by quantum coherence or entanglement, implementing near-infinite quantum

parallelism. These interactions perform computations and, at some point, the qubits all

collapse, or reduce to a single set of classical bits---the "solution".

Significant technological and commercial advantages are offered by quantum computers

if they are ever actually constructed (prototypes now exist, and research activity isintense). But regardless, theoretical aspects of quantum computing teach an enormous

amount about fundamental physics, and possibly consciousness.

The essential feature in quantum computing is superposition---each qubit may be in

superposition of both 1 and 0. What exactly is superposition? How are we to understand

this basic feature of unobserved quantum particles? How can something be in two places

or two states at once?

Roger Penrose explains superposition in the following way. According to Einstein's

general relativity, mass is equivalent to curvature in fundamental spacetime geometry.

The fundamental feature is not mass, but spacetime geometry. Mass existing in one

particular location or state is ("in reality") one particular curvature in fundamental

spacetime geometry.

Figure 7. According to Einstein's general relativity, mass is equivalent to curvature in spacetime

geometry. Penrose applies this equivalence to the fundamental Planck scale. The motion o f an object

between two conformational states of a protein such as tubulin (top) is equivalent to two curvatures

in spacetime geometry as represented as a two-dimensional spacetime sheet (bottom).

Now consider quantum superposition. In Penrose's view superposition of a particle in two

states or locations implies superposition of two different spacetime curvatures---anunstable separation, or bubble in spacetime itself.


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Figure 8. Mass superposition, e.g. a protein occupying two different conformational states

simultaneously (top) is equivalent, according to Penrose, to simultaneous spacetime curvature in

opposite directions - a separation, or bubble ("blister") in fun damental spacetime geometry.

Quantum computation would therefore be an organized process of separations and

reductions at the fundamental level---reconfiguring the basic level of spacetime

geometry. If qualia are embedded at this same basic level, then some form of quantum

computation in the brain could access fundamental qualia and select particular patterns ofconscious experience.

Figure 9. Are mental 'qualia' like the redness of a rose fundamental patterns in spacetime geometry?

This connection between the brain and fundamental spacetime geometry could patch the

age-old controversy. Socrates and Democritus were both right---consciousness requires

brain processes which access and select fundamental qualia embedded at the basic level

of spacetime geometry. Our conscious experience could derive from some basic process

rippling through reality.

5. Conclusion: Is consciousness due to computational emergence or fundamental

quantum process?

The burning issue is thus whether or not conscious experience like feelings, qualia, our

"inner life" can be accommodated within present-day science. Those who believe it can

(e.g. physicalists, reductionists, materialists, functionalists, computationalists,

emergentists) - like Socrates - see conscious experience as an emergent property of

complex neural network computation. Others see conscious experience either outside

science (dualists), or like Democritus believe science must expand to include conscious

experience as a primitive feature of nature, something like spin or harge (idealists,

panpsychists, pan-experientialists, pan-protopsychists).

Here is how (from an admittedly biased perspective) computational emergence views

stack up against quantum approaches in attempting to explain the enigmatic features of

consciousness.

Feature 1: 'Qualia', experience, hard problem (e.g. Chalmers, 1996a; 1 996b)

Computational emergence: Postulate conscious experience emerging from critical level

of neuronal computational complexity.

Unanswered: What is the critical level? Why should emergent phenomenon have

conscious experience? What causes transition from pre-conscious processes to

consciousness itself?

Quantum approaches: May philosophically subscribe to panexperientialism, or pan-

protopsychism following e.g. Spinoza, Leibniz, Whitehead, Wheeler and Chalmers.

Experience, qualia are deemed fundamental, a basic property of the universe like spin or

charge, perhaps rooted at the Planck scale.

Unanswered: What are fundamental properties? What unifying principle exists

(we don't want a new fundamental property for every conceivable experience).

How can the brain link to the quantum level or Planck scale?

Feature 2: Binding, unity in vision and imagery, sense of self, 'oneness'


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Computational emergence: Coherent neural membrane activities (e.g. coherent 40 Hz)

bind by temporal correlation of neural firing.

Unanswered: Why should temporal correlation bind qualia when different

features processed asynchronously are nonetheless somehow consciously

experienced as synchronous? (Zeki, 1998).

Quantum approaches: Macroscopic quantum states (e.g. Bose-Einstein condensates)are single entities, not just temporally correlated. Unity is provided through non-locality -

components are intimately connected and governed by a single wave function.

Unanswered: How can macroscopic quantum states exist in the brain and interact

with neural structures?

Feature 3. Transition from pre-conscious processes to consciousness itself

Computational emergence: Conscious experience emerges at a critical threshold of

neural activity?

Unanswered: What is the critical level? Why is the emergent phenomenon

"conscious"? What is the essential difference between non-conscious, or pre-

conscious neural processes, and conscious neural processes?

Quantum approaches: Pre-conscious processes are in quantum superposition of possible states. The process by which the possibilities reduce/collapse to definite

states is the transition between pre-conscious and conscious processes.(e.g. Stapp,

Penrose-Hameroff)

Unanswered: How is the quantum superposition manifest in the brain? What

is the cause of collapse? How is the output implemented by neural structures?

Feature 4: Non-computability (Penrose argues from Godel's theorem that human

thought has a non-computable component - some feature which is neither algorithmic

nor random/probabilistic).

Computational emergence: What non-computability?

Unanswered: How do we differ from computers?

Quantum approaches: Penrose quantum gravity collapse (objective reduction) ofthe wave function is proposed to be non-computable (influenced by Platonic

influences ingrained in spacetime geometry).

Unanswered: How does objective reduction link to the brain?

Feature 5: Free will (The problem in understanding free will is that our actions seem

neither deterministic nor random (probabilistic). What else is there in nature?

Computational emergence: Doesn't offer much help. Processes are either

deterministic or random. Questions existence of free will.

Unanswered: Everything.

Quantum approaches: Penrose 's objective reduction ("OR") is a possible solution.

Conscious actions are products of deterministic processes acted on at moments of

reduction by non-computable 'Platonic' influences intrinsic to fundamental spacetimegeometry.

Unanswered: How are Platonic influences represented? How do they

influence neuronal structures?

Feature 6: Subjective time flow. Physics has no requirement for a forward flow of

time, yet our conscious experience seems to have a flow of time.

Computational emergence: Agnostic - no position.

Unanswered: Why does time seem to flow?


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Quantum approaches: Quantum state reductions/collapses are irreversible. A series

of quantum reductions would "ratchet" through time to give an experience of time

flow.

Unanswered: Where, how in the brain could quantum state reductions occur?

Feature 7. Reverse time anomalies. Research by Ben Libet in the late 70's and

recent work by Dean Radin and Dick Bierman suggest that somehow the brain canrefer information (or qualia) backwards in time.

Computational emergence: No position - refute/explain away data.

Unanswered: What's wrong with the data interpretation leading to

conclusions regarding backward time referral? If experimentally corroborated,

how can backwards time referral be explained?

Quan tum approaches: Intervals between quantum state reductions are 'atemporal',

and reductions may send quantum information backwards through time.

Unanswered: How do reductions occur? How is quantum information

processed? Are qualia equivalent to quantum information?

So in an admittedly biased survey, quantum approaches are far better equipped to

deal with the enigmatic features of consciousness than are conventionalcomputationalist emergent approaches.

It is probably inevitable that the brain/mind be compared to a quantum computer. The

brain/mind has been historically compared to the current most advanced form of

technological information processing. In ancient Greece the mind was compared to a

seal ring in wax', in the 19th century a telegraph switching circuit, and in the 20th

century a hologram, and presently to the most deeply developed and successful

metaphor - the classical computer. If quantum computers become technological

reality and supercede classical computers as our most advanced form of information

processing technology, the brain/mind will be expected to be at least equally

advanced, and hence utilize some type of quantum computation. Even if quantum

computers do not become successful technology, their mere theoretical existence has profound implications for fundamental physics, and consciousness.


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Outline

Pan-protopsychism

The fundamental nature of reality

Is there a connection between the brain and "funda-mental" reality?

Illustrations

Penrose's Three Worlds (after Popper) 3worlds.jpg

The 'quantum foam' (from Kip Thorne) foam.jpgThe 'Casimir force' casimir.jpg

String theory string.gif

Violin analogy for string theory violin.jpg

Quantum geometry portrays spacetime as a woven fabric fabric.jpg

Planck scale spin networks may be the basic level of reality spinnet.jpg

Mass equivalent to spacetime curvature spacecurv.jpg

Superposition is equivalent to separation (bubble, or blister) in spacetime geometry spacecurv1.jpg

Classical and superpositioned spacetime geometry spacecurv2.jpg

Classical and superpositioned mass/spacetime form 'qubits' useful in quantum computation.

spacecurv3.jpg

1. Pan-protopsychism

If computational emergence is unable to account for conscious experience and other enigmatic features of

consciousness, what approach can do so?A line of panpsychist, panexperiential philosophy stemming from Democritus suggests that proto-

conscious experience is fundamental. In the past 100 years quantum theory and modern physics have

examined the basic nature of reality, and at the millenium these two avenues may be converging.

An extreme panpsychist view is that consciousness is a quality of all matter: atoms and their subatomic

components having elements of consciousness (e.g. Spinoza, 1677; Rensch, 1960). "Mentalists" such as

Leibniz and Whitehead (e.g. 1929) refined this position, contending that systems ordinarily considered to

be physical are constructed in some sense from mental entities. Leibniz (e.g. 1768) saw the universe as an

infinite number of fundamental units ("monads") each having a primitive psychological being. Whitehead

(e.g. 1929) described dynamic monads with greater spontaneity and creativity, interpreting them as mind-

like entities of limited duration ("occasions of experience" each bearing a quality akin to "feeling").

Bertrand Russell (1954) described "neutral monism" in which a common underlying entity, neither

physical nor mental, gave rise to both. More recently Wheeler (e.g. 1990) described a "pre-geometry" of

fundamental reality comprised of information.

Chalmers (1996a;1996b) contends that fundamental information includes "experiential aspects" leading to

consciousness. Chalmers coined the term "pan-protopsychism" to allow for an interaction between the

brain and fundamental entities producing consciousness as we know it. Consciousness could be a product

of the brain's interaction with fundamental reality.

Idealism is the notion that "consciousness is all there is". That is, our conscious minds create the external

world. A problem for idealism is intersubjective agreement, how elements of reality usually thought of as

'external' or 'physical' are common to any conscious being. This is also known as the problem of

"solipsism', which occurs in approaches in which the self is the total of existence. Universal mind may

address this concern, as agreement might be arrived at through sharing thoughts rather than a physical

reality. The challenge is then to explain why some elements are shared and others are absolutely private.

In Eastern traditions, universal "Mind" is often seen as fundamental, accessible to the brain (e.g. Goswami,

1993). And some Buddhist meditative disciplines portray consciousness as sequences of individual,

discrete events; trained meditators describe distinct "flickerings" in their experience of reality (Tart, 1995).

Buddhist texts portray consciousness as "momentary collections of mental phenomena", and as "distinct,

unconnected and impermanent moments which perish as soon as they arise." Each conscious moment

successively becomes, exists, and disappears - its existence is instantaneous, with no duration in time, as a

point has no length. Our normal perceptions, of course, are seemingly continuous, presumably as we

perceive "movies" as continuous despite their actual makeup being a series of frames. Some Buddhist

writings even quantify the frequency of conscious moments. For example the Sarvaastivaadins (von

Rospatt, 1995) described 6,480,000 "moments" in 24 hours (an average of one "moment" per 13.3 msec),

and some Chinese Buddhism as one "thought" per 20 msec. Perhaps not surprisingly, these times


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correspond nicely with neurophysiological events such as coherent 40 Hz (~ 25 msec), and are consistent

with proposals for quantum state reductions in the brain (as we shall see in later lectures).

This suggests not only that consciousness is a sequence of discrete events (experienced continuously,

perhaps in a way like a movie is perceived continuously despite being comprised of discrete frames), but

also that consciousness is serial! Recent evidence suggests that visual consciousness is indeed serial. See:

If qualia are embedded in fundamental reality accessible to the brain, perhaps Platonic values may be thereas well. Plato in 400 B.C.: "...ideas have an existence...an ideal Platonic world...accessible by the intellect

only...a direct route to truth...". In "Shadows of the Mind" Penrose (1994) described three worlds: the

physical world, the mental world and the Platonic world. The physical world and the mental world are

familiar and agreed upon as actual realities clearly, the physical world exists and thoughts exist.

Penrose's Platonic world includes mathematical truths, laws and relationships, as well as primitives for

aesthetics and ethics---affecting our senses of beauty and morality. The Platonic world appears purely

abstract. Could it simply exist in the empty space of the universe? If essential aspects of truth and beauty

are indeed fundamental, perhaps the Platonic world is ingrained at the most basic level of reality along with

qualia (perhaps qualia and Platonic values are the same?).

A problem for realistic Platonism is that concepts like truth and beauty would seem to be culturally-loaded,

complex abstractions constructed according to experience and built up from a vast multitude of simpler

generalizations and categorizations. But perhaps what is embedded in fundamental reality are primitive

elements of these complex abstractions, distributed nonlocally through spacetime geometry.Another objection is that Platonic values should be experienced in the same way by everyone. But we don't

all like the same food, or favorite movie star. However Platonic values would be interacting with varying

cultural, genetic, memory and other influences to give a final response. Plus, fundamental patterns in

spacetime geometry and Platonic values embedded there may be evolving over time (as suggested by Lee

Smolin in "Life of the Cosmos").

Figure 1. Penrose's 3 worlds (after Popper) "In some way, each of the three worlds, the Platonic

mathematical, the physical, and the mental, seems to mysteriously emerge from---or at least berelated to---a small part of its predecessor (the worlds being taken cyclically)." Shadows of the Mind.

But could qualia and Platonic values be embedded in spacetime geometry, in empty

space? What is empty space?

2. The fundamental nature of reality

As described briefly in Week 1, the nature of space and time has also been debated since

the ancient Greeks. Democritus (who thought 'atoms' were the basic constituents of

matter) saw space as a true, empty void through which matter traveled. On the other

hand Aristotle saw empty space containing a background pattern, which he termed the

'plenum'. In the 19th century consideration of how electromagnetic waves travel through

a vacuum led Maxwell to propose his "luminiferous ether", however the famous

Michelson-Morley experiment seemed to refute such an idea and support again the notionof a true void. Einstein's special relativity with no preferred frames of reference also

came down on the side of a true void. However Einstein's general relativity with

spacetime curvature weighed in on the side of a background pattern in spacetime which

Einstein termed the 'metric'. Since then numerous ideas and theories have attempted to

describe some makeup of fundamental spacetime geometry.

A branch of quantum field theory known as quantum electrodynamics (QED) predicts

that virtual particles and waves (virtual photons, matter-antimatter pairs) continuously


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wink into and out of existence (e.g. Jibu and Yasue, 1995; Seife, 1997). These are

quantum fluctuations that impart dynamic structure to the vacuum. The energy of the

virtual particles contributes to the zero-point energy of the vacuum.

At a much higher-energy (or equivalently, much smaller in scale) level, fluctuations in

the topology of spacetime lead to what is described as the "quantum foam".

Figure 2. The "quantum foam": Quantum fluctuations in the topology of spacetime produce a foam

of erupting and collapsing superpositions of spacetime topologies. (from Thorne, 1994)

This picture of the quantum vacuum had been developed by Max Planck and Werner

Heisenberg in the 1920's. In 1948 the Dutch scientist Hendrick Casimir predicted that the

all-pervading zero point energy could be measured using parallel surfaces separated by a

tiny gap. Some (longer wavelength) virtual photons would be excluded from the gap

region, Casimir reasoned, and the surplus photons outside the gap would exert pressureforcing the surfaces together. Recently, this "Casimir force" was quantitatively verified

quite precisely (Lamoreaux, 1997), confirming the zero point energy. Lamoreaux's

experimental surfaces were separated by a distance d ranging from 0.6 to 6 microns, and

the measured force was extremely weak (Figure 3a).

Figure 3. A: The Casimir force of the quantum vacuum zero point fluctuation energy may be

measured by placing two macroscopic surfaces separated by a small gap d. As some virtual photonsare excluded in the gap, the net "quantum foam" exerts pressure, forcing the surfaces together. In

Lamoreaux's (1997) experiment, d1 was in the range 0.6 to 6.0 microns (~1500 nanometers). B: Hall

(1996; 1997) calculated the Casimir force on microtubules. As the force is proportional to d-4, and

d2 for microtubules is 15 nanometers, the predicted Casimir force is roughly 106 greater on

microtubules (per equivalent surface area) than that measured by Lamoreaux. Hall calculates a

range of Casimir forces on microtubules (length dependent) from 0.5 to 20 atmospheres.

Could the Casimir force have biological influence? At the Tucson II conference,

physicist George Hall (Hall, 1996; 1997) presented calculations of the Casimir force on

model cylinders representing biological microtubules which form networks within

neurons and other cells. Hall considered the microtubule hollow inner core of 15

nanometers diameter as the Casimir gap d. (Hall assumed microtubules are

electroconductive; recent experiments have shown this to be true). As the force is predicted to be proportional to d-4, Hall's models predict significant pressure (0.5 to 20

atmospheres) exerted by the quantum vacuum on microtubules of sufficient length

(Figure 3b). Microtubules actually are under compression in cells, a factor thought to

enhance vibrational signaling and tensegrity structure (e.g. Ingber, 1993). In the well

known phenomenon of "pressure reversal of anesthesia," unconscious, anesthetized

experimental subjects wake up when ambient pressure is increased on the order of 10 to


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100 atmospheres. This implies that a baseline ambient pressure such as the Casimir force

acting on microtubules as suggested by Hall may be required for consciousness.

Despite these measurable effects, the fundamental nature of spacetime and the unification

of general relativity and quantum mechanics remain elusive. However several approaches

to the deepest structure of spacetime have emerged. What is known is that the Planck

scale (10-33 cm, 10-43sec) is the scale at which spacetime is no longer smooth, butquantized.

One approach is string theory, or superstrings, begun by John Schwarz of CalTech and

Michael Green of Queen Mary College in London in the 1980's. The theory combines

general relativity and quantum mechanics, and also can explain exotic entitites which

comprise all particles in the universe.

String theory states that quarks, electrons and other particles of matter, rather than being

point-like, are actually tiny "line-like" objects called strings. The strings are incredibly

small---each is approximately the size of the Planck length (10-33 cm), the smallest

possible distance in spacetime, one billionth of one billionth the radius of an electron.

Just as the strings of a violin can vibrate in many ways to produce varying musical notes,

the tiny strings in spacetime can vibrate in many ways to create the different types ofelementary particles. Strings also potentially explain the force-carrying particle/waves

(e.g. bosons) which act on matter. Further, as the strings move within curved spacetime,

string theory may unify general relativity and quantum mechanics.

Figure 4. String theory predicts matter and forces arise from vibrating Planck scale strings (Science

Year 2000)

Figure 4a. Vibrations of fundamental strings are proposed to result in particles and energy, like the

vibrations of violin strings produce sound. String theory predicts that the strings can exist in two basic forms---open and closed.

Strings interact by splitting and joining, and with vibratory motion can thus determine the

particles and forces which make up the universe.

The problems with string theory are that 1) it is currently untestable, and 2) it requires 10

or 11 dimensions. Do these extra dimensions actually exist, or are they mathematicalabstractions with no basis in reality?

Another approach to the fundamental nature of reality which requires only 4 dimensional

spacetime is quantum geometry (Figure 5). To provide a description of the quantum

mechanical geometry of space at the Planck scale, Penrose (1971) introduced "quantum

spin networks" in which spectra of discrete Planck scale volumes and configurations are

obtained (Figure 6). Ashtekar, Rovelli and Smolin have generalized these spin networks

to describe quantum gravity. These fundamental spacetime volumes and configurations


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may qualify as philosophical (quantum) monads. Perhaps quantum gravity Planck-scale

spin networks encode proto-conscious experience and Platonic values?

Figure 5. Quantum geometry - the tiniest units of space consist of a complex fabric of interwoven

threads which give rise to the spacetime continuum (Science Year 2000)

Figure 6. A quantum spin network. Introduced by Roger Penrose (1971) as a quantum mechanical

description of the geometry of space, spin networks describe spectra of discrete Planck scale volumes

and configurations (with permission, Rovelli and Smolin, 1995).

There are reasons to suspect gravity, and in particular quantum gravity in the

fundamental makeup of spacetime geometry.

Roger Penrose: "The physical phenomenon of gravity, described to a high degree of

accuracy by Isaac Newton's mathematics in 1687, has played a key role in scientific

understanding. However, in 1915, Einstein created a major revolution in our scientific

world-view. According to Einstein's theory, gravity plays a unique role in physics for

several reasons (cf. Penrose, 1994). Most particularly, these are: 1) Gravity is the only

physical quality which influences causal relationships between space-time events.

2) Gravitational force has no local reality, as it can be eliminated by a change in space-

time coordinates; instead, gravitational tidal effects provide a curvature for the very

space-time in which all other particles and forces are contained.

It follows from this that gravity cannot be regarded as some kind of "emergent

phenomenon," secondary to other physical effects, but is a "fundamental component" of

physical reality. It may seem surprising that quantum gravity effects could plausibly have

relevance at the physical scales relevant to brain processes. For quantum gravity is

normally viewed as having only absurdly tiny influences at ordinary dimensions.

However, we shall show later that this is not the case, and the scales determined by basic

quantum gravity principles are indeed those that are relevant for conscious brain

processes.

Perhaps we may view the elusive quantum gravity as the basic makeup of fundamental

spacetime geometry. But how is it connected to brain processes?

3. Is there a connection between the brain and 'fundamental' reality?

In David Bohm's approach, fundamental qualia might play the role of the quantum

potential. Bohm's approach will be discussed in Week 5 by Paavo Pylkkanen.

Another approach is that of Michael Conrad's, called the fluctuon model. This is

summarized in a paper accompanying this lecture.

In the approach taken by Roger Penrose, Einstein's general relativity is combined with

aspects of quantum theory to give a process (Objective Reduction:OR) occurring at the

fundamental level of spacetime geometry.


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Penrose: (from "Conscious events as orchestrated spacetime selections")

~http://www.u.arizona.edu/~hameroff/hardfina.html

According to modern accepted physical pictures, reality is rooted in 3-dimensional

space and a 1-dimensional time, combined together into a 4-dimensional space-time.

This space-time is slightly curved, in accordance with Einstein's general theory ofrelativity, in a way which encodes the gravitational fields of all distributions of mass

density. Each mass density effects a space-time curvature, albeit tiny.

This is the standard picture according to classical physics. On the other hand, when

quantum systems have been considered by physicists, this mass-induced tiny

curvature in the structure of space-time has been almost invariably ignored,

gravitational effects having been assumed to be totally insignificant for normal

problems in which quantum theory is important. Surprising as it may seem, however,

such tiny differences in space-time structure can have large effects, for they entail

subtle but fundamental influences on the very rules of quantum mechanics.

Figure 7. According to Einstein's general relativity, mass is equivalent to curvature in spacetime

geometry. Penrose applies this equivalence to the fundamental Planck scale. The motion of an object

between two conformational states of a protein such as tubulin (top) is equivalent to two curvatures

in spacetime geometry as represented as a two-dimensional spacetime sheet (bottom).

Figure 8. Mass superposition, e.g. a protein occupying two different conformational states

simultaneously (top) is equivalent, according to Penrose, to simultaneous spacetime curvature in

opposite directions - a separation, or bubble ("blister") in fundamental spacetime geometry.

Penrose (continued):

Superposed quantum states for which the respective mass distributions differ

significantly from one another will have space-time geometries which

correspondingly differ. Thus, according to standard quantum theory, the superposed

state would have to involve a quantum superposition of these differing space-times.

In the absence of a coherent theory of quantum gravity there is no accepted way of

handling such a superposition. Indeed the basic principles of Einstein's general

relativity begin to come into profound conflict with those of quantum mechanics (cf.Penrose, 1996). Nevertheless, various tentative procedures have been put forward in

attempts to describe such a superposition. Of particular relevance to our present

proposals are the suggestions of certain authors (i.e., Karolyhazy, 1996; 1974;

Karolyhazy et al., 1986; Kibble, 1991; Di'si, 1989; Ghirardi et al, 1990; Pearle and

Squires, 1995; Percival, 1995; Penrose, 1993; 1994; 1996) that it is at this point that

an objective quantum state reduction (OR) ought to occur, and the rate or timescale of

this process can be calculated from basic quantum gravity considerations. These


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particular proposals differ in certain detailed respects, and for definiteness we shall

follow the specific suggestions made in Penrose (1994; 1996). Accordingly, the

quantum superposition of significantly differing space-times is unstable, with a

lifetime given by that timescale. Such a superposed state will decay - or "reduce" -

into a single universe state, which is one or the other of the space-time geometries

involved in that superposition.Whereas such an OR action is not a generally recognized part of the normal quantum-

mechanical procedures, there is no plausible or clear-cut alternative that standard

quantum theory has to offer. This OR procedure avoids the need for "multiple

universes" (cf. Everett, 1957; Wheeler, 1957, for example). There is no agreement,

among quantum gravity experts, about how else to address this problem.

So Penrose OR is a self-organizing process in fundamental spacetime geometry. If that is

where qualia and Platonic values are embedded, an OR process occurring in the brain

could be the connection.

Figure 9. Quantum coherent superposition represented as a separation of space-time. In the lowest

of the three diagrams, a bifurcating space-time is depicted as the union ("glued together version") of

the two alternative space-time histories that are depicted at the top of the Figure. The bifurcating

space-time diagram illustrates two alternative mass distributions actually in quantum superposition,

whereas the top two diagrams illustrate the two individual alternatives which take part in the

superposition (adapted from Penrose, 1994 - p. 338).

Figure 10. Superpositions and qubits (qubits are information "bits" which can exist and compute

while in superposition, then reduce to a classical output state). A. Protein qubit. A protein such as

tubulin can exist in two conformations determined by quantum London forces in hydrophobic

pocket (top), or superposition of both conformations (bottom). B. The protein qubit corresponds to

two alternative spacetime curvatures (top), and superposition/separation (bubble) of both curvatures

(bottom).

In conclusion, Penrose OR may be the connection between the brain and 'fundamental'

reality. Consciousness may involve self-organization of spacetime geometry stemming

from the Planck scale.

The question of whether such a process could actually occur in a biological environment

will be discussed in future lectures.

Browne, M.W. 1997. Physicists confirm power of nothing, measuring force of universal

flux. The New York Times, January 21, 1997.

Chalmers, D. (1996) Facing up to the problem of consiousness. In: Toward a Science of

Consciousness - The First Tucson Discussions and Debates, S.R. Hameroff, A. Kaszniak

and A.C. Scott (eds.), MIT Press, Cambridge, MA.


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Chalmers, D. (1996) Toward a Theory of Consciousness. Springer-Verlag, Berlin.

Conze, E., (1988) Buddhist Thought in India, Louis de La Vallee Poussin (trans.),

Abhidharmako"sabhaa.syam: English translation by Leo M. Pruden, 4 vols (Berkeley) pp

85-90.

Diosi, L. (1989) Models for universal reduction of macroscopic quantum fluctuations.

Phys. Rev. A. 40:1165-1174.Everett, H., (1957) Relative state formulation of quantum mechanics. In Quantum Theory

and Measurement, J.A. Wheeler and W.H. Zurek (eds.) Princeton University Press, 1983;

originally in Rev. Mod. Physics, 29:454-462.

Goswami, A., (1993) The Self-Aware Universe: How Consciousness Creates the Material

World. Tarcher/Putnam, New York.

Hall, G.L. 1996. Quantum electrodynamic (QED) fluctuations in various models of

neuronal microtubules. Consciousness Research Abstracts -Tucson II (Journal of

Consciousness Studies) Abstract 145.

Ingber D.E. 1993. Cellular tensegrity: Defining new roles of biological design that

govern the cytoskeleton. J Cell Science 104(3):613-627.

Jibu, M., Yasue, K. 1995. Quantum brain dynamics: an introduction. John Benjamins,Amsterdam.

Jibu M, Pribram K.H., Yasue K 1996. From conscious experience to memory storage and

retrieval: The role of quantum brain dynamics and boson condensation of evanescent

photons. Int J Modern Physics B 10 (13&14):1735-1754.

Jibu, M., Hagan, S., Hameroff, S.R., Pribram, K.H., and Yasue, K. (1994) Quantum

optical coherence in cytoskeletal microtubules: implications for brain function.

BioSystems 32:195-209.

Pearle, P. (1989) Combining stochastic dynamical state vector reduction with

spontaneous localization. Phys. Rev. D. 13:857-868.

Pearle, P., and Squires, E. (1994) Bound-state excitation, nucleon decay experiments and

models of wave-function collapse. Phys. Rev. Letts. 73(1):1-5.Penrose, R. (1987) Newton, quantum theory and reality. In 300 Years of Gravity S.W.

Hawking and W. Israel (eds.) Cambridge University Press.

Penrose, R. 1971. in Quantum Theory and Beyond. ed E.A. Bastin, Cambridge

University Press, Cambridge, U.K.

Penrose, R. (1989) The Emperor's New Mind, Oxford Press, Oxford, U.K.

Penrose, R. (1994) Shadows of the Mind, Oxford Press, Oxford, U.K.

Penrose, R. (1997) On understanding understanding. International Studies in the

Philosophy of Science 11(1):7-20, 1997.

Rovelli C, Smolin L 1995b. Spin networks in quantum gravity. Physical Review D

52(10)5743-5759.

Seife, C. 1997. Quantum mechanics. The subtle pull of emptiness. Science 275:158.Shimony, A., 1993. Search for a Naturalistic World View Volume II. Natural Science

and Metaphysics. Cambridge University Press, Cambridge, U.K.

Tart, C.T., (1995) personal communication and information gathered from "Buddha-1

newsnet"

von Rospatt, A., (1995) The Buddhist Doctrine of Momentariness: A survey of the

origins and early phase of this doctrine up to Vasubandhu (Stuttgart: Franz Steiner

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Wheeler, J.A. (1990) Information, physics, quantum: The search for links. hIn (W. Zurek,

ed.) Complexity, nEntropy, and the Physics of Information. Addison-Wesley.


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Lecture 2Interpretations of quantum mechanics

and the nature of reality

Classical physics, as it had developed up to the end of the 19th century, saw that there are

two basic kinds of entities in the universe, particles and fields. The particles were thought

to follow Newton's laws of motion, while the fields where thought to obey Maxwell'sequations for the electromagnetic field. Lord Kelvin said that physics was pretty much

finished except that there were two small clouds in the horizon, the negative results of the

Michelson-Morley experiment (the search for ether) and the failure of Rayleigh-Jeans

law to predict black-body radiation. Lord Kelvin chose his clouds well for the former

gave rise to relativity and the latter to the quantum theory.

The ontologically essential lesson of the quantum theory was that the classical idea of

particles and fields was wrong. The electromagentic field turned out to have a particle

aspect, and particles like the electron turned out to have a field aspect. The most

fundamental ontological feature of the quantum theory then is that each manifestation of

matter and energy can have two possible aspects, that of a wave and that of a particle.

This is philosophically significant because it is a universal feature The debate about theinterpretation of the quantum theory has to do with how to deal with this observed fact of

wave-particle duality.

Quantum theory began when it was discovered that the electromagentic field has a

particle aspect in the sense that it exchanges energy with particles in small discrete

amounts or quanta. Thus light (previously thought to be a form of wave motion due to

observed diffraction and interference effects) was thought to consist of particles or

photons with energy E = hf when it interacts with matter (h is Planck's constant and f is

frequency of the wave aspect of the light). This is paradoxical because the energy of a

bullet of light is expressed in terms of frequency which is a wave property. So a light

bullet is no ordinary bullet. The energy of the particle aspect of light is determined by the

frequency of its wave aspect. This is completely against anything that was encountered inclassical physics. Particles like electrons were initially thought to be like little bullets

which circulate around the nucleus pretty much like the planets circulate around the sun.

It was possible to measure typical particle properties like mass and charge for the

electron. However, it was discovered that the electron - and all subatomic particles - also

have a wave aspect.

This can be clearly seen in the well-known two-slit experiment. (If you are not familiar

with this, check out the brilliant web site of the University of Colorado:

go to the atomic lab and choose the

two-slit experiment.)

Because the quantum theory is often presented in the spirit of the Copenhagen

interpretation which emphasizes indeterminacy and probability, people sometimesoverlook very simple facts regarding the wave properties of the electron. Note first that

the interference pattern which is built up spot by spot is very determinate - so there is

"statistical causality" at the quantum level, not just indeterminacy of the behaviour of the

individual system. The key question to ask is is why we get an interference pattern rather

than some other pattern or no definite pattern at all (which one might expect if electrons

were truly indeterminate in their behaviour). Classically we would expect just "two piles"

of electrons behind the screen, rather than the observed interference fringes or "many


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piles" with regions of no electrons between them. It is just a basic experimental fact that

we get an interference pattern which can be predicted with the mathematics of wave

motion. The reasonable way to think about this is to say that there is a wave aspect

associated with each electron and that this wave aspect is causally powerful in that it

makes sure that the particle aspect of each individual electron obeys the interference

pattern, never going to the "forbidden regions".However, one must watch out not to think of this wave as just an ordinary wave of

classical physics. For one thing for the many-body system the wave lives in a 3N+1

dimensional "configuration space", where N is the number of systems that we are

considering and the additional dimension is time. Also, because of the uncertainty

principle it is not possible to observe how an individual electron is moving under the

guidance of the wave, and thus the idea of such movement and guidance is thought often

to be "metaphysical" - a mere hypothesis without the possibility for experimental

verification. The standard view has been to think of the quantum wave as a kind of

probability wave.

The participants of this course have no doubt very different backgrounds in their

knowledge of quantum mechanics. The world wide web provides a good resource forintroductions and visualizations of the various ideas. One good brief description of the

standard view of quantum mechanics is the piece "Some Basic Ideas about Quantum

Mechanics by Stephen Jenkins at

and it is recommended that you read this at this point if you are not familiar with the

standard view. For a more technical account of the Copenhagen interpretation of quantum

mechanics, check John G. Cramer at

Non-locality vs. Non-reality

The EPR Paradox and Hidden Variables

In one version of the famous thought experiment due to Einstein, Podolsky and Rosen(1935), a neutral pion (p 0) decays into an electron (e-) and a positron (e+):

p 0 3/4 ® e- + e+

Because the neutral pion is spinless, quantum mechanics prescribes that the two decay

products must have opposite spin. Until a measurement is made on one member of the

duo, say the electron, there is equal probability that the measurement will yield an "up"

or a "down" result. However measuring "up" spin for the electron then implies that the

positron must have "down" spin; measuring "down" spin for the electron implies that the

positron must have "up" spin. And this must hold regardless of how far apart the electron

and positron were when the measurement was made. Experiments of this kind have been

performed in actuality (Aspect, Grangier and Roger, 1982; Aspect, Dalibard and Roger,

1982) and the results have proven to be completely consistent with quantum mechanics.

Figure 1 [EPR] One possible realization of the Einstein-Podolsky-Rosen

Gedankenexperiment. Measuring "up" spin for the electron immediately implies that the


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positron must have "down" spin, and vice versa, regardless of how far apart they might be

when measured.

Einstein, Podolsky and Rosen (EPR) assumed in their analysis of the thought experiment

that no non-local influence could instantaneously inform the positron that a measurement

had been made on the electron (after all, it was Einstein who introduced the Theory of

Special Relativity that formalized the notion of a locality constraint), so they concludedthat the spin of the positron must be a "real" property (a position known as quantum

realism), determined by variables that had not been or perhaps could not be measured -

so-called hidden variables. Their contention was that quantum mechanics was

"incomplete"; that the probabilistic distribution of spin measurements determined by

experiments was a result of our ignorance of these hidden variables. In their view, if we

knew the values of the hidden variables, the results of measurements would be given

deterministically, just as in classical mechanics.

Von Neumann (1932) was the first to put forward a theorem to the effect that hidden

variable theories consistent with the predictions of quantum mechanics were impossible.

Working from the density matrix formalism that is widely believed to stand or fall with

quantum mechanics itself, von Neumann established that no quantum mechanicalensemble is dispersionless. (A dispersionless ensemble is one for which the square of the

average value for any observable is equal to the average value of the observable squared.)

Although this theorem could at best prove only that non-dispersive hidden variable

theories were impossible, von Neumann believed that such theories were the only kind

that had to be eliminated from consideration in order to establish his thesis. Only this

kind of hidden variable theory, the non-dispersive kind, could eliminate the statistical

element from quantum mechanics and reduce it to the kind of classical theory that would

allow one to predict the results of individual acts of observation. But his theorem

overlooked the possibility that if the hidden variables were themselves of a statistical

nature (dispersive) then, even though the statistical element would not be eliminated from

quantum mechanics, it could nevertheless be made compatible with a local, causaldescription of how one could understand the spin of the electron and positron in the EPR

thought experiment. It was not until almost thirty years later that Bell proposed a similar

theorem (Bell, 1964, 1966) that made it much more clear what assumptions had to be

made about hidden variable theories in order to eliminate them from consideration.

Bell's Theorem

Bell's theorem demonstrated that quantum mechanics was in fact not compatible with

hidden variables, at least not if you wanted the hidden variables to be real properties

determined locally; that is, if you wanted to interpret hidden variables as having some

determinate value regardless of whether or not there was a 'measurement situation' and if

you wanted that determinate value to depend only on the 'particle' being measured. To

accommodate the predictions of quantum mechanics, as borne out by experiment, eitherthe reality or the locality assumption must be relaxed.

To demonstrate this, Bell starts from the same EPR thought experiment with the

modification that the spin, of both the electron and the positron, can be measured along

any specified direction. Bell's theorem will then be a statement about the average value

that one obtains when the two spin measurements, one on the electron and one on the

positron, are multiplied.


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If the hidden variables can be given local instantiation then they can be assigned a

probability density and the average of the product of spin measurements can be

determined in a prescribed way.

If it is true, as asserted by hidden variable theories, that the outcomes of all possible

experiments that might be performed on the electron/positron system are simultaneously

well-defined (as would be the case if these outcomes were decided by hidden variablestaking real values that were simply unknown to us), then it should be possible to write

consistent mathematical statements simultaneously invoking both the actual

measurement of the positron spin and counterfactual measurements, ones that might have

been made but were not. Thus the mathematical statement that Bell derives incorporates

the EPR reality assumption that the result of a measurement is determined whether or not

the measurement is made.

Bell's conclusion is that for any theory involving local hidden variables a certain

inequality must always hold, an inequality that involves the average product of electron

and positron spin measurements made under various alignments of the measurement

apparatus, at least some of which must be counterfactual. The actual inequality is rather

cumbersome regardless which of several different formulations one chooses. One of the possible versions (Clauser et al., 1969) states that the positive difference between the

average products calculated when the measurement devices (for electron and positron

respectively) are aligned along directions a and b, and when they are aligned along

directions a and c, must be less than or equal to two plus or minus the sum of the average

product obtained when the devices are aligned along directions d and c, and when they

are aligned along d and b (directions a, b, c and d being arbitrary). A mouthful, to be

sure.

Figure 2 [Bell] In the formulation due to Clauser et al. (1969), Bell's theorem can be

given this graphical representation, where each depiction of an EPR-type experiment

represents the average product of electron and positron spins calculated for the alignment

of detectors shown. For particular choices of the alignments a, b, c and d, Bell's

inequality is violated by the predictions of quantum mechanics.

In particular cases this statement, derived under the assumption that the hidden variables

of EPR must be both real and local, can be shown to be in contradiction with the

predictions of quantum mechanics. Either quantum mechanics is wrong or there is no

room for local hidden variables.

The experiments of Aspect et al. (Aspect, Grangier and Roger, 1982; Aspect, Dalibardand Roger, 1982) have shown the predictions of quantum mechanics to be correct in

cases where a violation of Bell's inequality is incurred. The experimental design made it

possible to ascertain that this result holds even in situations where the particles being

measured (these were actually two correlated photons rather an electron and a positron,

but the principle is the same) were separated such that no possible signal could have

informed the second particle of the measurement result on the first, prior to the second

being itself measured.


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Since the premise of Bell's theorem, that it is possible to write a theory that gives a

complete description of the state by introducing hidden variables that are instantiated

locally, leads to a false conclusion, we have a reductio ad absurdum indicating that the

premise must also be false.

Whether the premise is false because it assumes the locality of the variables or because it

assumes the reality of the variables is currently a topic of lively debate. Stapp (1997) has,for instance, introduced an argument that, if correct, would indicate that it is in fact the

locality assumption that is at fault, for he derives a contradiction similar to that of Bell,

apparently without assuming the reality of any hidden variables. This is a particularly

strong claim, one that would herald significant changes in the way physicists think about

natural phenomena. Equally though it is one to which there has been great resistance in

the physics community since, whenever non-local influences obtain in an experimental

situation, the sphere of causal influence can no longer be restricted. (This should not, of

course, be taken as any argument against Stapp's contention, since what physicists would

like to be true presumably has no influence on what actually is.) For this reason

considerable controversy surrounds Stapp's claim.

At issue is the use that the argument makes of counterfactuals (Mermin, 1997; Unruh,1997; Stapp, 1998). Counterfactual reasoning is ubiquitous in classical science and plays

a recognized role in theorizing about the quantum domain as well, however the principles

of quantum mechanics must preclude certain uses that would be valid in classical

reasoning and it is not a matter of general agreement where the line should be drawn. The

concern is that, if counterfactuals have been employed in a quantum mechanical situation

to which they would be inappropriate, then a reality condition has been smuggled into the

argument implicitly. If this were the case then Stapp's argument would reach the same

conclusion as Bell's theorem. One avenue of exploration that may be interesting in this

regard is the proposal made by Griffiths (1996, 1998) of a set of conditions - framed in

terms of consistent histories - that would ensure that orthodox logic could be applied

consistently in quantum contexts. In a recent addition to the debate, Stapp (1999) himselfhas invoked this framework in defence of his argument.

Non-collapse Interpretations

Bohm's interpretation

Bohm's interpretation will be presented in more detail in lecture 5, so here is just a brief

summary. Bohm had written a textbook "Quantum Theory" (1951) in which he attempted

as far as possible to give a physical formulation for the quantum theory while staying

within the then standard "Copenhagen" view. Many physicists like Pauli and Einstein

thought that he had done a great job, yet he felt he didn't really understand the theory.

One puzzling question was that of ontology. Quantum theory didn't provide a clear

ontology, yet by making the so called WKB approximation one could derive classical

mechanics out of quantum mechanics, thus also obtaining the straightforward classicalontology. Considering this Bohm saw that if one didn't make the approximation one

could obtain a "quantum ontology", where there was an extra potential added to the

classical ontology.

Physically this meant that one could imagine the electron as a particle always

accompanied by a new kind of wave that gave rise the new "quantum potential" acting on

the particle. He went on to show in his well known 1952 Physical Review papers that you

can explain basic features of non-relativistic quantum theory by assuming that the


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electron is such an entity with two aspects: a particle aspect which explains why we

observe a particle-like manifestation every time we observe the electron, and a wave

aspect which acts on the particle in a subtle way, thus explaining why the particle aspect

obeys the mathematics of wave motion and why electrons collectively produce

interference patterns, without the need to assume the collapse of the wave function. The

theory was a non-local "hidden variable" theory and was thus a counter-example to von Neumann's proof that hidden variables are impossible. It met initially with great

resistance but is today, in various developed forms, considered as one of the serious

alternative interpretations of the quantum theory.

Everett's interpretation

Hugh Everett III's interpretation of quantum mechanics (Everett, 1957, 1973), or 'relative

state' theory, despite being the interpretation most often celebrated in fiction, has been

largely misinterpreted in popular accounts, at least with respect to Everett's original

proposal and this has in part been due to the fact that later adherents imposed their own

reading of the theory. While some of these are worthy of consideration in their own right,

much of the criticism directed against Everett's interpretation has in fact objected to

aspects that did not appear in the original version.Like Bohm's interpretation, Everett's involves no 'collapse of the wave function'. But

unlike Bohm, Everett accepts the 'reality' of quantum superposition. The heart of Everett's

proposal is in fact that superposition obtains in every case and at every level of

description, whether the object of description is the spin state of an electron, the state of a

pointer in a measuring instrument or even the state of the experimenter's mind looking at

a measurement device.

Everett proceeds from the observation that collapse is not really a necessary element of

quantum mechanics if there exists a means to establish rigorous correlations between

superpositions at various levels.

Imagine for instance that an electron, existing in a superposition of 'up' and 'down' spin

states, is 'measured'. For Everett, this means that the superposition of spin states of theelectron leads to a similar superposition in the measuring device, say a superposition of

the word 'up' being printed and of the word 'down' being printed. The measurement

situation provides an association between the 'up' state appearing in the superposition of

electron states and the 'up' state appearing in the superposition of measurement device

states. This can be taken even further so that when the experimenter looks at the printed

output, her mind also enters a superposition of states involving a state in which she reads

the word 'up' and a state in which she reads the word 'down'. Again there is an association

between elements of the superposition at the level of the printout and elements of the

superposition at the level of the experimenter's mind. From the perspective of any one of

these superposed minds however, there appears to be no superposition at all. That is

because the conscious state of the experimenter has become entangled with the state ofthe printout in such a way that the conscious state in which the word 'up' is read is always

accompanied by the state of the measurement device in which the word 'up' is printed.

Because the mind is not outside the superposition, but rather itself superposed, the

experimenter exists in one mental state or the other and so sees only the word 'up' or the

word 'down' rather than a superposition of both.

This has been taken to imply that, since there are now two observers, the universe itself

has bifurcated, each of the resulting branch universes accommodating only one of these


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observers. The thought behind this is that there is only one 'me' in this universe and any

other versions of 'me', that might perhaps remember different results in a quantum

mechanics experiment, should go find their own universe. On this reading, every time a

'measurement' is made, the universe must similarly 'split' (hence the designation 'many-

worlds interpretation'). It is this ontologically prodigious contention that has been

repeatedly criticized as extravagant excess. It gives no account of the process whereby a'split' might occur and one cannot therefore raise the relevant concerns. Is it appropriate

to raise an objection on the basis of energy conservation? Or perhaps with respect to the

'no-cloning theorem' (according to which the information completely specifying a

quantum system cannot be copied from that system without destroying the original)? Or

simply as regards parsimony? Without further information, the interpretation would

appear too under-specified to decide. Even if splitting turns out to be unobjectionable in

itself, there nevertheless remains the problem of deciding what exactly should constitute

the 'measurement' that provokes the split. The measurement problem that initially

prompted the quest for an interpretation of quantum mechanics remains thus an

unresolved paradox. All of this however pertains to a reading that cannot be traced to

Everett's work and may be largely credited to a sympathetic misconstrual by DeWitt(1970, 1971).

Albert and Loewer (1989; also Albert, 1992), Lockwood (1989) and Chalmers (1996)

have urged a reading that eschews the objective splitting of the universe. On this version

a single universe evolves a vast superposition: electrons, measuring devices and human

minds all added to the mix. Superposition of observers is treated no differently from any

other case of superposition and prompts no bifurcation of worlds but the world takes on a

classical appearance relative to any one of the superposed observers (hence 'relative-state'

theory).

One of the abiding difficulties with even this more reasonable version is the problem of

preferred basis. The relative-state interpretation assumes a basis in which, relative to the

mind of an observer, the mutually exclusive outcomes of quantum experiments alwaysshow up as discrete classical alternatives. This is not a unique possibility, for the mind of

the observer might just as well be correlated with one of two mutually exclusive

superpositions, in which event the world would not retain its classical appearance. But no

justification can be given for denying the possibility without the introduction of new

principles.

Neither does the interpretation give us any understanding of the amazing ability of the

quantum mechanical calculus to predict the probabilities of various outcomes,

probabilities that are borne out in statistical trials. In collapse interpretations of quantum

mechanics, the squared modulus of each coefficient in the wave function determines the

relative probability of realizing the corresponding term upon collapse. Since the wave

function in relative-state theory never collapses, it is not clear how one might recover this principle, obviating the need for further assumptions.

Everett himself addressed the problem by introducing a 'measure' over the space of

observers. This measure weights each branch of the wave function with the standard

quantum mechanical probability, but the measure is explicitly introduced as an abstract

and uninterpreted quantity, and specifically not as a probability measure. Everett goes on

to show that the set of observers who would not find a statistical distribution of results

consistent with quantum theoretical predictions, has measure zero, the implication being


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that such observers will never occur. As pointed out by d'Espagnat (1976), the

implication follows however, only if the measure is interpreted in terms of probability.

The measure then appears as either an ad hoc adjustment to square the theory with the

predictions of quantum mechanics or, minimally, as a further assumption. Since no

objective realization of the measure is supplied, there is no way to argue that the

implication follows from the significance of the measure.In an attempt to give objective meaning to the measure and to cement the implication,

Albert and Loewer, in their 'many-minds' version, interpret the weighting as occurring in

a space of actual minds. They begin in a manner reminiscent of DeWitt's 'many-worlds'

view, but assume that it is not worlds that split but minds, and that the branching minds

are all unaware of each other. This shift allows them room to define minds such that

superposition fails as applied to them. Minds are ideal candidates as they appear never to

be in superposition. It is thus the splitting of minds that, in an over-all random process, is

weighted by the quantum mechanical probabilities, so that the probabilities are realized

as relative proportions of an ensemble of minds that, according to the circumstance, may

be vast or even infinite in number. The 'many-minds' picture thus avoids the problem of

preferred basis - minds sit outside the principle of superposition, and themselves definethe favored basis in which the split occurs - but as in the DeWitt interpretation, we have

again a problem of extravagance. If it is already a problem to explain how one conscious

state might arise from one brain state, then the problem is clearly compounded by

imagining that one brain state gives rise to a vast, potentially infinite, number of

conscious states.

Collapse and 'Collapse-like' Interpretations

Decoherence

The theory of decoherence was originated by Murray Gell-Mann and James Hartle

(1989) to contend with problems surrounding the interpretation of quantum mechanics in

a specifically cosmological context. While cosmology may not be an evident concern in

consciousness studies, the theory of decoherence has attained considerable prominencewith respect to certain of the proposed models. In reviewing this interpretation, it will be

important to bear in mind its origins in cosmology and how that has shaped it in a

specific image.

Cosmologically, it is difficult, if not impossible, to maintain the line between 'observer'

and 'observed' postulated in those interpretations that make a sharp "cut" between

quantum and classical. That is, we do not expect, given the extreme nature of the ambient

conditions immediately following the Big Bang, that the early universe was inhabited by

nascent consciousnesses. Particularly if we are to take seriously some form of cognitive

coherence - that consciousness obtains only where it is correlated with a physical entity

capable of sensing, cognizing and reacting to its environment - the postulation of

primordial observers seems clearly problematic. Observers, at least biological observers,would seem to require perhaps billions of years of interceding evolution to facilitate their

appearance on stage. Are we to imagine then that until such time as biological entities

evolved to the level of consciousness that the entire universe remained in perpetual

superposition?

Wheeler (1957), at one time, put forward exactly this hypothesis: that the appearance of

conscious observers in the superposition of all possibilities collapsed the wave function

of the universe retroactively, thus creating in a sense the entire classical history of all that


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is. While perhaps intriguing from the perspective of recursion and certainly grand in

scope, the hypothesis repudiates key features of the formulation of quantum mechanics.

The 'observer' in Wheeler's proposal is not outside the phenomenon 'observed' -

conscious observers appear within the superposition - so the divide between classical and

quantum, a divide initiated by Bohr and carried through von Neumann, Heisenberg, Dirac

and Wigner, has been abandoned. This means that a quantum system must be able toinitiate its own collapse, but if this can be facilitated then there may be no reason to

single out consciousness as a factor. We may find a route more amenable to expression in

the context of standard physical theory.

Decoherence is an attempt to do just that. 'Measurement' is regarded as a specific case of

a process that is going on all the time, effecting the reduction of quantum to classical

without the necessary involvement of conscious entities.

Gell-Mann and Hartle (GH) build a theory of decohering histories. They attempt to show

that, in what they call a quasi-classical domain, a quantum superposition of histories can

be made to decohere to a single, approximately classical history. Each possible history is

assigned a probability of being actualized quasi-classically but the theory must

nevertheless preserve the quantum superposition of histories wherever coherence is acritical factor in the explanation of empirical results (as in the two-slit experiment, for

instance).

Histories are defined in the theory in terms of projection operators. These operators,

acting on state vectors, project out particular properties at a given time. At any particular

Webcourse (1999) - Quantum Approaches to Understanding the Mind

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